Optimal Dividend, Reinsurance, and Capital Injection Strategies for an Insurer with Two Collaborating Business Lines

This paper analyzes a bivariate optimal dividend problem for an insurer with two collaborating business lines under a diffusion model with correlated Brownian motions. The framework incorporates dividend payouts, proportional reinsurance, and inter‑line capital transfers to prevent bankruptcy. The authors provide complete analytical solutions, identifying three scenarios with closed‑form value functions and optimal strategies. Results show a threshold dividend policy, with the more important line having a lower threshold. Optimal reinsurance decreases with aggregate reserves and stabilizes after a switching point. Correlation between lines affects reinsurance, and the capital transfer rule is consistent across scenarios.